Severe limits on variations of the speed of light with frequency

Explosive astrophysical events at high redsfiift can be used to place severe limits on the fractional variation in the speed of light with frequency (Delta c/c), the photon mass (m(gamma)), and the energy scale of quantum gravity (E-QG). I find Delta c/c < 6.3 x 10(-21) based on the simultaneous arrival of a flare in GRB 930229 with a rise time of 220 +/- 30 mu s for photons of 30 and 200 keV. The limit on m(gamma) is 4.2 x 10(-44) g for GRB 980703 from radio to gamma ray observations. The limit on E-QG is 8.3 x 10(16) GeV for GRB 930131 from 30 keV to 80 MeV photons.